Well, the proper way is to terminate both cables on a split block, then run a patch cable with solid wires and punch them down to the appropriate pairs on that same block. There are 2,3,4 and 6 pair split blocks that are perfect for this application. Obviously with outdoor installations, the block will need to be contained within some kind of proper weatherproof enclosure, like an AT&T B-CSC, C-CSC or D-CSC.
Honestly, with regard to the grounding of pins 7/8, I've never really checked. I seriously doubt that anybody even worries about that anymore. I know for sure that on indoor installations, Verizon never does anything with pins 7/8.
Shielded cable includes a drain wire. The drain wires from each cable should be joined together at the block and connected to a suitable ground connection. It is usually easiest to punch these drain wires down on the bottom two rows of clips on the block and just bridge them together. That way, a single pair jumper wire can be used to make the final connection to a suitable ground.
Many of today's outdoor T1 network interfaces include both screw/IDC terminals and an RJ48X jack per circuit. That way, you still have the option to terminate separate cable pairs with minimal effort. These also include a CPE grounding terminal in them to accommodate the drain wires.
Yes, a standard 8P8C plug will work just fine for this application.
